DNS and LES of primary atomization of turbulent liquid jet injection into a gaseous crossow environment

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DNS and LES of primary atomization of turbulent liquid jet injection into a gaseous crossow environment

Anirudh Asuri Mukundan, Giovanni Tretola, Thibaut Ménard, Marcus Herrmann, Salvador Navarro-Martinez, Konstantina Vogiatzaki, Jorge César

Brändle de Motta, Alain Berlemont

To cite this version:

Anirudh Asuri Mukundan, Giovanni Tretola, Thibaut Ménard, Marcus Herrmann, Salvador Navarro- Martinez, et al.. DNS and LES of primary atomization of turbulent liquid jet injection into a gaseous crossow environment. Proceedings of the Combustion Institute, Elsevier, In press,

�10.1016/j.proci.2020.08.004�. �hal-02950068�

DNS and LES of primary atomization of turbulent liquid jet injection into a gaseous crossow

environment

Anirudh Asuri Mukundan

, Giovanni Tretola

, Thibaut Ménard

, Marcus Herrmann

, Salvador Navarro-Martinez

, Konstantina Vogiatzaki

,

Jorge César Brändle de Motta

, Alain Berlemont

a

CNRS UMR6614-CORIA, Saint Etienne du Rouvray, 76801, France

b

Imperial College London, 58 Princes Gate, Kensington, London SW7 1AL, UK

c

Advanced Engineering Centre, University of Brighton, Brighton BN2 4GJ, UK

d

Université de Rouen Normandie, Saint Etienne du Rouvray, 76801, France

e

School for Engineering of Matter, Transport and Energy, Arizona State University, P.O. Box 876106, Tempe, AZ 85287-6106, USA

Abstract

In this paper, we study the primary atomization characteristics of liquid jet injected into a gaseous crossow through direct numerical simulations (DNS) and large eddy simulations (LES). The DNS use a coupled level set volume of uid (CLSVOF) sharp interface capturing method resolving all relevant scales to predict the drop size distribution (DSD) for drops larger than the grid spacing. The LES use a volume of uid (VOF) diused in- terface method modelling the sub grid droplets. The purpose of this paper is to provide a comparison of the results of drop data between DNS and LES. The simulations are performed for a liquid jet injection with liquid-gas momentum ux ratio of 6.6 , liquid jet Reynolds number of 14,000 injected

∗

Corresponding author:

Email addresses: [email protected] (Thibaut Ménard),

[email protected] (Salvador Navarro-Martinez)

into a crossowing air with Reynolds number 570,000 and Weber number of 330 at a liquid-to-gas density ratio of 10 . Two distinct and simultane- ous atomization/breakup mechanisms have been observed in the simulations:

column/bag breakup and ligament/surface breakup. It was found that the DSDs obtained from the DNS and LES each follow a log-normal distribution based on their respective droplet diameter data. An overlap region exists between the individual DSDs from the DNS and LES when combined. The width of this overlap region decreases along the downstream direction. A log-normal distribution is found to be a good t to the combined DSD incor- porating both resolved and sub-grid droplets. This information is relevant for the secondary atomization simulations and modeling.

Keywords:

Atomization, Crossow, Interface capture, Stochastic elds, Drop size distribution

1. Introduction

With the growing number of long-haul passenger aircraft, it has become

necessary to develop more ecient aircraft engines that can oer long range

with reduced pollutant emissions. The amount of pollutants produced de-

pends on the completeness of the fuel combustion which is linked to the

quality of injected liquid fuel atomization. Atomization is the process of

disintegration of the coherent liquid structure into droplets. In fact, small

droplets promote quick evaporation and better mixing with the oxidizer,

while large drops may deposit on the walls of the engine chamber thereby

lowering the combustion eciency and eventually harming the engine. Hence,

it is imperative to understand and gain control of the atomization process.

To that end, a commonly employed injection conguration in aero engines called liquid jet in crossow is chosen for the investigation in this study. In this conguration, the liquid fuel injected into a crossowing gaseous environ- ment atomizes into droplets. There have been multiple experimental inves- tigations [1, 2] for this conguration to understand the breakup mechanisms [3], to classify the breakup regimes [4], to characterize the jet penetration [5, 6], and to gain understanding of the jet dynamics [7]. For a complete review, the reader is referred to the work of Broumand and Birouk [8].

There have also been several numerical studies, for example, Herrmann [9] performed detailed numerical simulations of primary atomization of an experimentally investigated liquid jet in crossow conguration [3]. The grid dependence of the droplet diameters [9], the eect of the density ratio on the atomization characteristics [10] and the jet dynamics [11] have been investi- gated in the past. The eect of inow velocity proles on the atomization characteristics have been investigated by Ghods and Herrmann [12] using three dierent velocity proles (in-nozzle large eddy simulations (LES), fully developed turbulent velocity proles each with, and without nozzle geom- etry) under two dierent density ratio operating conditions. These studies found that the jet penetration was in agreement with the experimental cor- relation of Wu et al. [5] for the case of turbulent inow velocities taking the injector geometry into account. Furthermore, they found that the liq- uid column was more deformed when using a fully developed turbulent pipe inow without nozzle geometry than when including the nozzle geometry.

The results conrm the observations of Brown and McDonell [3] that the

initial velocity prole has a high impact on the atomization characteristics.

Owkes et al. [13] used LES to investigate the eect of rounded and sharp edged nozzle exits on the atomization characteristics. They found excellent agreement between the simulations and experiments of Gopala [14] for both the nozzle geometries and reasonable match of the droplet sizes with exper- imental data. Recently, Li and Soteriou [15, 16] investigated the eects of liquid fuel density, viscosity, and intermeditate Weber number on the liquid jet penetration, evolution of Sauter Mean Diameter (SMD) as a function of crossow direction, and jet dynamics of the crossow atomization.

The direct numerical simulations (DNS) approach provides a complete de- scription of the ow dynamics, but its high computational cost limits its use to ows with moderate Reynolds and Weber numbers and liquid-gas density ratio. LES on the other hand has cheaper computational cost but requires modeling of the sub grid (or unresolved) multiphase turbulence dynamics.

Despite the numerous eorts, there has not been a direct comparison of DNS

and LES for the liquid jet in crossow injection conguration. This paper

presents, for the rst time, the direct comparison of results of primary atom-

ization of turbulent liquid jet injected into a subsonic gaseous crossow. The

DNS in this study is to be considered as quasi-DNS without sub-grid scale

model in capturing the small droplets (due to under-resolution). However,

it resolves all relevant processes [17, 18] to predict drop sizes larger than the

mesh spacing but does not resolve the Kolmogorov scales for both the phases

in a classical sense of DNS. The operating condition chosen in this work is

comparable to that of a practical aero engine. The non-dimensional num-

bers such as liquid-gas momentum ux ratio, Reynolds, and Weber numbers

follow the experimental study of Brown and McDonell [3]. This study aims to investigate and contrast the dierent atomization and breakup character- istics, jet penetration, and drop size distributions (DSDs) between DNS and LES.

This paper is organized as follows. The governing equations solved in DNS and LES along with the numerical methods of the respective ow solvers and phase interface capturing methods are presented in Section 2. This is followed by the presentation of the liquid jet in crossow conguration, case setup, and operating conditions in Section 3. Finally, the results obtained from the simulations are presented and discussed in Section 4 from which the conclusions are drawn in Section 5.

2. Governing Equations and Numerical Methods 2.1. DNS

To describe the multiphase ow with DNS, the pressure and velocity elds of the ow are obtained by solving the following conservative form of the incompressible Navier-Stokes equations,

∇ · u = 0, (1)

∂(ρu)

∂t + ∇ · (ρu u) = −∇P + ∇ · (2µD) + T

, (2) where ρ is the density, u is the velocity eld, P is the pressure eld, µ is the dynamic viscosity, D =

(∇u +∇

u) is the strain rate tensor and T

is the surface tension force acting on the location of the liquid/gas interface x

.

The interface is captured using a coupled level set volume of uid (CLSVOF)

method [19] in which the location of the interface x

is described by a scalar

level set signed distance function φ proposed by Osher and Sethian [20]. The value of φ(x, t) > 0 denes the liquid phase (uid 1), φ(x, t) < 0 denes the gas phase (uid 2), and φ(x

, t) = 0 denes the location of the interface.

The fraction of the liquid volume within a computational cell is represented by the liquid volume fraction scalar F . The advection of the interface is achieved by solving the following transport equation for Ψ = [φ, F ]

:

∂ Ψ

∂t + u · ∇Ψ = 0, (3) The physical properties of the phases α in a compuational cell is determined using F as α(x) = α

F (x) + α

(1 − F (x)) . This expression involves an as- sumption that the physical properties are constant within each phase where α is either density ρ or viscosity µ with the indices 1 and 2 denoting the respec- tive uid properties. A directionally-split advection method [21] is used to solve Equation (3). This approach is implemented in the in-house ow solver ARCHER [19, 22, 23] with consistent mass and momentum ux computation [22]. A staggered variable arrangement with scalar quantities stored at the cell center and vector quantities at the cell faces is employed in ARCHER. A second-order central dierence scheme is employed for discretization of the spatial derivatives and fth-order WENO scheme for convective term with second-order Runge-Kutta scheme for temporal advancement of the Navier- Stokes equations. For more details, the reader is referred to Vaudor et al.

[22]. The physics of atomization of the coherent liquid jet into droplets of

varying sizes are captured by solving these equations. All the droplets are de-

scribed in the Eulerian framework and no transfer to Lagrangian descriptions

is employed in the DNS.

2.2. LES

In the case of LES, a Σ - Y -PDF approach is employed to solve the incom- pressible Navier-Stokes equations. This approach consists of solving the joint probability density function (jPDF) transport equation of liquid volume and surface density using stochastic methods [24]. A system of stochastic partial dierential equations (SPDE) is derived from the PDF transport equations using N stochastic elds, where each stochastic eld has its own liquid volume fraction F

(instead of the mass fraction Y

) and surface density Σ

where n ∈ {1, 2, . . . N} . The advantage of this approach is that it can simulate both dense and dilute regions of the spray.

Using the Ito formulation [25], the following transport equations for the stochastic elds are obtained,

dF

dt + ¯ u

∂F

∂x

= ∂

∂x

D

∂F

∂x

+ p

2D

∂F

∂x

dW

dt , (4)

dΣ

dt + ¯ u

∂Σ

∂x

= ∂

∂x

D

∂Σ

∂x

+ p

2D

∂Σ

∂x

dW

dt + S (5) where S is the source term, D

is the sub-grid scale (SGS) diusivity which is proportional to the SGS viscosity ν

according to the relation D

= ν

/Sc

with a SGS Schmidt number of Sc

= 1 . In this equation, dW

represents a Wiener process with mean 0 and variance equal to ∆t

. The solution of Equations (4) and (5) allows to obtain the moments of the PDF equations. The rst-moments are computed as

F ¯ = 1 N

N

X

n=1

F

, Σ = ¯ 1 N

N

X

n=1

Σ

. (6)

If all the moments are known, Equations (4) and (5) are equivalent to the

LES ltered counterpart [24]. After the stochastic eld equations have been

advanced in time, all relevant parameters can be obtained directly. For ex- ample, the characteristic fragment length per stochastic eld is the Sauter Mean Diameter (SMD) is dened as

d

= 6 F

(1 − F

)

Σ

, (7)

where the corresponding ltered moment d ¯

can be obtained directly from Equation (6). The DSD (in space and time) can then be obtained directly from binning the SMD values.

The source term S is modelled as a non-linear restoration to equilibrium term as proposed by Lebas et al. [26],

S = Σ

τ

1 − Σ

Σ

, (8)

where Σ

is the equilibrium surface density and τ is the associated relaxation time-scale related to the ow [24]. At high Weber numbers typical of spray atomization, the time scale can be LES-scale based on the ltered strain rate, τ ∝ || S ¯

||

, or proportional to a turbulent time scale (as in the Reynolds Averaged Navier-Stokes approach). Capillary eects in the source term are restricted to the local value of Σ

, which can be characterized by a critical Weber number [27] as We

= 2k

(ρ

+ ρ

)F (1 − F )/(σΣ

) , where k

is the local sub-grid scale turbulent kinetic energy and following Navarro- Martinez [24], We

= 1 is used in this work.

The Σ - Y -PDF approach is implemented in the nite volume open source

software OpenFOAM [28]. The spatial derivatives for the momentum equa-

tion are approximated by standard second-order central dierences. The mo-

mentum equations are integrated using a second-order Crank-Nicolson tem-

poral scheme. The WALE [29] method is used to model the sub grid stress

terms using ν

since it did not introduce excessive diusion for this congu- ration. The stochastic elds are solved using an operator-splitting technique with the MULES scheme [30] for the convective step to minimise numerical diusion and central derivatives for diusive processes. The Ito formulation is retained in this work. The spatial gradient appearing in the stochastic terms of Equations (4) and (5) in the Ito formulation is approximated using central dierences. The temporal term of the Ito process is discretized using the Euler-Maruyama scheme [31]. The Wiener process is modelled with a weak approximation as dW

= η

∆t

, where η

is a {−1, 1} dichotomic random vector [32]. The resultant scheme is weakly consistent of order ∆t

[31] and the number of elds chosen in the simulations is N = 16 following Navarro-Martinez [24]. Similar to DNS, no Lagrangian transformation of droplets is performed in the LES.

3. Operating Condition and Computational Domain

The operating condition for the simulations (both DNS and LES) used in this work has been studied experimentally by Brown and McDonell [3]

and numerically by Herrmann [9] previously. Table 1 summarizes the values

of the physical quantities of the liquid and gas phase. It is to be remarked

that although the liquid-to-gas density ratio r

is articially reduced in the

simulations (by modifying liquid velocity, viscosity, and density), all the non-

dimensional numbers, i.e., liquid-gas momentum ux ratio q , Reynolds num-

ber Re, and Weber number We of the liquid and gas phases remain the same

as in the experiments. It is to be noted that all the details mentioned in this

section apply to both DNS and LES unless otherwise stated explicitly.

Table 1: Operating conditions and non-dimensional numbers

Quantity Simulation

Jet diameter ( D

) [mm] 1.3 Jet density ( ρ

) [kg/m

] 12.25 Jet velocity ( U

) [m/s] 97.84 Jet viscosity ( µ

) [kg/ms] 1.11 × 10

Surface tension ( σ ) [N/m] 0.07 Crossow gas density ( ρ

) [kg/m

] 1.225 Crossow gas velocity ( u

) [m/s] 120.4 Crossow viscosity ( µ

) [kg/ms] 1.82 × 10

Density ratio ( r

) 10

Momentum ux ratio ( q ) 6.6

Jet Weber number (We

) 2178 Jet Reynolds number (Re

) 14,079 Crossow Weber number (We

) 330 Crossow Reynolds number (Re

) 570,000

The computational domain chosen in this work is of size 40D

× 10D

× 20D

[17] where D

is the diameter of the liquid jet. This domain is smaller than in the experiments [3], however, as observed from previous numerical studies [911], the domain size reduction does not aect the primary breakup description.

In the case of DNS, a uniform structured Cartesian mesh containing about

262 million cells is used for discretizing the computational domain. This re-

sults in a uniform mesh spacing of ∆x = ∆y = ∆z = D

/32 throughout the domain. While in the case of LES, a Cartesian mesh composed of ap- proximately 2.5 million cells is employed. The grid is rened in the region close the liquid inlet and then stretched (at 3 % cell expansion ratio) along the crossow downstream direction resulting in a computational cell size Λ in the range of D

/32 to D

/8 with Λ

= D

/32 near the injection region.

Since an implicit ltering technique with the computational mesh as lter is employed in LES, the lter width is the cubic root of the computational cell volume.

Both the DNS and LES use a fully developed turbulent pipe ow velocity prole at the inlet of the liquid jet. The liquid jet at t

= tU

/D

= 0 is initialized in the DNS as a cylinder of diameter D

and height 4∆x protruding into the crossow channel. While in LES, the initial domain is empty at t

= 0 and the injection starts from t

> 0 . The reported results from the simulations in the following sections are non-dimensionlized using the jet velocity U

and jet diameter D

as reference quantities unless otherwise explicitly mentioned. The simulations are performed up to t

= 73 (in DNS) and t

= 75 (in LES) with data stored approximately every t

= 1.3 .

4. Results and Discussion

Figure 1 shows instantaneous snapshots of the side view of the liquid

jet from DNS and LES. In the DNS (Figure 1a), the interface is sharp and

is indicated by the zero level iso-contour of the level set function φ . The

droplets atomized from the liquid core of the jet and the instability waves

formed on the liquid jet column can be clearly seen in Figure 1a. However,

in the case of LES (Figure 1b), due to the diused nature of the interface, the iso-contour of F ¯ = 0.5 is an indication of where the mean interface could be but not the exact location of the interface. The droplet breakup occurs at large as well as small scales however those at large scales are not visible in the visualization (c.f. Figure 1b) since the interface is diused. Moreover, a part of the small scale breakup occurs in sub-grid scales and hence such sub-grid droplets are also not visible in the visualisations.

The DNS and LES results revealed two main simultaneous atomization mechanisms: column/bag and ligament/surface breakup. The instabilities that are formed predominantly on the windward side of the liquid jet col- umn generate roll-ups that continue to grow along the jet nally forming bag-like structure. Such structures break, forming varying sized droplets, thus, called column/bag breakup [9]. In addition, ligaments are seen strip- ping o the sides of the liquid column in the simulations. This phenomenon is seen as surface rupture in the literature [9], thus, its name ligament/sur- face breakup. Such ligaments undergo further breakup into droplets due to Rayleigh-Plateau instability. These observations of the breakup mechanisms are consistent with the literature [9, 11].

The instability waves generated on the windward side of the liquid jet

column are responsible for the droplet and ligament breakup. The plots of

the contour of liquid volume fraction from DNS and LES shown in Figure 2

clearly depicts these instability waves as the corrugations on the windward

side of the liquid jet. These contour plots are obtained at the mid-plane

location along the spanwise direction (direction perpendicular to both liquid

injection and crossow) in the computational domain. In fact, the waves are

(a) DNS (b) LES

Figure 1: Instantaneous snapshots of the side view of the atomizing liquid jet obtained from DNS and LES.

profoundly visible in the DNS result (Figure 2a) due to the sharp interface capture while the diused interface capture is demonstrated in the LES result (c.f. Figure 2b). The reader is referred to the study of Asuri Mukundan et al.

[18] for a detailed analysis of these instability waves.

(a) DNS (b) LES

Figure 2: Instantaneous snapshots of liquid volume fraction from DNS and LES in the near-injector region.

Next, we analyze the mean jet penetration obtained from the DNS and

LES results. The mean jet penetration and bending gives a detailed repre-

sentation of the jet penetration probability which determines the size of the

combustion chamber in aero engines. In the DNS, the mean jet penetration

is obtained from the average of several instantaneous snapshots of the vi- sualization of the side view of the liquid jet. The rationale behind such an averaging procedure is to be consistent with that employed for the shadowg- raphy images from experiments. In the LES, since the interface is diused, the precise location of the interface is not clearly determined. Thus, the up- per jet plume boundary is determined as the locus of points for each line in the jet injection direction where the liquid volume fraction decreases below a threshold δ% of the local maximum value. In this paper, δ = 5 is chosen to determine the jet upper boundary. This method has been suggested for experimental analysis of the trajectory [3] and has been implemented nu- merically [33, 34]. Figure 3 shows the mean jet penetration from DNS and LES compared with the experimental correlations for validation. The jet plume boundary obtained from simulations are compared with the two ex- perimental correlations: Wu et al. [5] (valid in near-injector regions) given as z/D

= 1.37 (q x/D

)

and from Stenzler et al. [6] (valid in far-injector re- gions) given as z/D

= 2.63q

(x/D

)

We

µ

/µ

where

µ

correspond to the dynamic viscosity of the liquid used in the experi-

ments. On analyzing Figure 3, we see that simulation results qualitatively

agree with the experimental correlation of Stenzler et al. [6] (gray dashed

line) that that of Wu et al. [5] (green solid line). Such an agreement is

consistent with the observation from the literature [9]. As remarked by Her-

rmann et al. [11], the low value of the liquid-to-gas density ratio of 10 used

in this work (compared to the density ratio of 816 in experiments) is prone

to under-prediction of the jet penetration and bending in the simulations for

the near-injector correlation of Wu et al. [5].

0 1 2 3 4 5 6 7 8 9 10 0

1 2 3 4 5 6 7 8

x/D

z /D

Figure 3: Averaged side view snapshot of the liquid jet in crossow from DNS with exper- imental curve t. DNS(averaged image), LES ( ) Wu et al. [5] ( ), and Stenzler et al.

[6] ( ).

Besides the jet penetration and bending, the DSD is a vital quantity to

ascertain the quality of the primary atomization. Moreover, it is useful for

primary atomization modeling in which droplets are injected along a specic

liquid core path with a given velocity [35]. The DSDs are obtained from

the DNS and LES by post-processing the data after the total mass in the

computational domain is stabilized to indicate statistical steady state. The

droplets/liquid structures from the DNS are rst identied using a connected

component labelling (CCL) liquid structure detection algorithm in which the

cells belonging to each single liquid structure (i.e., droplets) are tagged and

labelled forming a cluster of cells for each liquid structure. The droplets

and their attributes are then collected for each structure (from all its com-

prising cells). The attributes include volume, surface area, volume averaged

coordinates of droplet centroid, and volume averaged velocity components at centroid. An equivalent spherical diameter of each droplet is obtained from its volume. The droplets are then sampled at specic downstream locations x/D

. The DSD is then generated by binning the drop diameters into 20 bins of equal size in terms of log(d

/D

) where d

represents the drop diameter. A total of 10,282 droplets were collected over all sampled time steps from the DNS. In the case of LES, due to the diused nature of the interface, no grid reslved droplets (drops larger than mesh spacing) are cap- tured. However, the sub-grid droplets are captured whose diameter values are determined from the Equation (7). The DSD is then generated by these diameter values using the same procedure as that of the DNS.

The droplets are sampled at the locations x/D

= 5, 10, 15, 20, 25, 30 from

the DNS and LES results. Figure 4 shows the individual plots of the DSD

from DNS and LES sampled at x/D

= 20 along with their log-normal

distribution ts (solid lines in the plots). It can be seen that the DSD span

over a nite range of the droplet diameters that are within the limits of DNS

and LES mesh spacings. A log-normal t (solid lines in Figures 4a and 4b)

to the DSD from the DNS and LES is observed to be a good model as also

observed by Herrmann [9]. It is to be remarked that the tting is made based

on the respective simulation data range, hence, the tting law parameters

are dierent for DNS and LES. The drops with diameters d

< 2∆x are

not well resolved in the DNS while the drops larger than Λ

(mesh spacing

at the sampling location x/D

= 20 ) are not found in the LES. Since the

DNS captures the mesh resolved droplets and LES characterizes the sub grid

droplets by construction of each simulation framework, the combined DSD

would determine the physical DSD. The rationale behind this idea is that either approach (i.e., DNS and LES) is good for one range of drop sizes so a combined DSD will give a good estimate of the true measure of the range of the droplet diameters belonging to resolved as well as sub-grid scales. This resulted in a direct comparison of the DSD between DNS and LES as shown in Figure 4c. This gure revealed that there is an overlap region of nite size [0.08D

, 0.2D

] for the droplet diameters. To get the model for the physical DSD, a log-normal distribution is found to be a reasonable t as shown by the solid line in Figure 4c capturing the large well resolved droplets from the DNS and small sub-grid droplets from the LES.

10

10

10

10

10

10

d

/D

PDF( d

/D

)

(a) DNS drop size distribu- tion

10

10

10

Λ20

d

/D

(b) LES drop size distribu- tion

10

10

10

d

/D

(c) Combined drop size dis- tribution

Figure 4: Drop size distribution from DNS ( ), LES ( ) with log-normal t ( ),

∆x ( ), 2∆x ( ), and Λ

( ) limits at x/D

= 20 .

Now, we analyze the plots of the DSDs from the DNS and LES sampled

at the other downstream locations shown in Figure 5. At all sampling loca-

tions, there exists a nite sized overlap region in the DSD: for x/D

= 5 it is

[0.055D

, 0.167D

] (Figure 5a), for x/D

= 10 it is [0.0563D

, 0.166D

] (Fig- ure 5b), for x/Dj = 15 it is [0.0579D

, 0.149D

] (Figure 5c), for x/D

= 25 it is [0.0584D

, 0.127D

] (Figure 5d), and for x/D

= 30 it is [0.0476D

, 0.131D

] (Figure 5e). Overall, it can be seen that the length of the overlap region re- duces downstream until the last sampling plane of x/D

= 30 which could indicate generation of a bimodal distribution of large and small droplets.

10

10

10

10

10

10

d

/D

PDF( d

/D

)

(a) x/D

= 5

10

10

10

d

/D

(b) x/D

= 10

10

10

10

d

/D

(c) x/D

= 15

10

10

10

10

10

10

d

/D

PDF( d

/D

)

(d) x/D

= 25

10

10

10

d

/D

(e) x/D

= 30

Figure 5: Drop size distribution from DNS ( ) and LES ( ) at dierent downstream sampling locations along with their respective log-normal ts ( ).

On one hand, the detection of drops with d

> 0.1D

shows the pres-

ence and importance of large drops that are not captured by the LES. On

the other hand, the presence of sub-grid droplets shows the signicant pres-

ence of small drops not captured by DNS. This wide range of scales needs to be considered when modeling primary atomization for liquid jet in crossow congurations. The agreement between the DNS and LES in the overlapping (or shared) range at all sampling locations (c.f. Figure 5) suggests that the sub-grid distribution observed from the LES can be reliable. The scales in- vestigated by DNS and LES are shown in Figure 6 displaying the schematic representation of the ideal limits of the droplet sizes depicted by the hatched region. This highlights the advantage of a combined DNS and LES study allowing to extract a wide of range of drop sizes for analyses and modeling of primary atomization processes.

Lx

40Dj

d^max_drop,DNS

0.5Dj Dj

2∆x Dj/16

∆x Dj/32

Λmax

0.4Dj

0.14Dj

d^max_drop,LES d^min_drop,LES

7Dj/1000

Physical &

Computational scales Jet diameter scale DNS resolved scales

LES sub grid scales LES resolved scales

Figure 6: Schematic of range of length scales of motion resolved by DNS and LES at x/D

= 20 with shared length scales shown in hatched region.

5. Conclusions

Results from direct numerical simulations (DNS) and large eddy sim-

ulations (LES) of the primary atomization of turbulent liquid jet injected

into subsonic gaseous crossow environment have been presented. The liq-

uid/gas interface has been reconstructed using a sharp coupled level set vol-

ume of uid (CLSVOF) method in DNS while a diused volume of uid

(VOF) method has been used in LES. The incompressible Navier-Stokes

equations have been solved directly without a sub-grid model in the DNS and a Σ - Y -PDF approach with WALE sub-grid scale model in the LES. Two simultaneous atomization mechanisms have been observed in the simulations:

column/bag breakup and ligament stripping/surface breakup at the sides of the jet. The column instability growth has not been captured in the LES due to diused nature of the interface. The liquid jet penetration and bending obtained from the DNS and LES qualitatively agree with the experimental correlation however under-predicting the bending. This under-prediction is attributed to the lower liquid-to-gas density ratio operating condition used in the simulations. Despite not being able to capture the interface dynamics exactly, the LES-PDF breakup predicts a similar sub-grid DSD as the DNS in the range 2∆x < d

< Λ . The DSDs obtained from DNS and LES follow log-normal distributions based on the respective simulation data. A combination of the DSDs from DNS and LES oers a wide range of length scales and gives a log-normal distribution as a good t. The results from this work are intended to be used as a starting point for further investigations of the eect of density and viscosity ratio on the atomization characteristics at higher mesh resolutions.

Acknowledgments

The funding for this project from the European Union`s Horizon 2020 re-

search and innovation programme under the Marie Skªodowska-Curie grant

agreement N° 675676 is gratefully acknowledged. The computing time at

CRIANN (Centre Régional Informatique et d'Applications Numériques de

Normandie) under the scientic project No. 2003008 and at GENCI-[TGCC/

CINES/IDRIS] (Grant2019-2613) are also gratefully acknowledged. The au- thors also acknowledge funding by the UK's Engineering and Physical Science Research Council support through the grant EP/S001824/1 (KV, GT).

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